Research On Generation And Self-detection Of Elliptical Vortex Light Based On Equivalent Spiral Lens

All photons carry spin angular momentum,and they may also carry orbital angular momentum.The beam with orbital angular momentum is called vortex light.There are many kinds of vortex light.Elliptical vortex light is one of the special types.Its light field has lost the circular symmetry,and some properties have been improved,such as the ability of anti air disturbance and particle control.Therefore,it can be applied in the field of space optical communication and particle control.This paper focuses on how to use the most convenient and effective method to generate and control vortex beams,especially elliptical vortices.The idea is to generate and control the vortex beams based on the characteristics of the wavefront modulated by the spatial light modulator.The main components include:(1)In this paper,the concept of the equivalent circular symmetric spiral lens is introduced,and the design idea of the equivalent circular symmetric spiral lens is given: the spherical lens,the phase spiral plate and the diaphragm are superposed equivalently,and the formula description of the superposed process is given,and the phase generation simulation is carried out by using MATLAB program,and the corresponding phase grayscale diagram is obtained.Then the physical process of plane wave passing through the equivalent circular symmetric spiral lens is simulated by MATLAB software.The simulation results show that the generated beam is the converging vortex light,the focal length of the beam is equal to the focal length of the superimposed spherical lens,and the cross-sectional light intensity shape of the light field is a ring.The radius of the ring can be adjusted by changing the topological load,focal length or the radius of the superimposed diaphragm of the equivalent spiral lens.(2)The cone lens is added to the equivalent circular symmetric spiral lens to obtain the equivalent perfect lens.When the incident beam is Gaussian,the transmission function and Fresnel Huygens integral formula are used to calculate the perfect vortex light.On the focal plane of the equivalent perfect lens,the radius of the ring is independent of the topological charge,which depends on the focal length and the cone angle of the conical lens.The simulation results with MATLAB software confirm the above conclusions.The simulation also includes the phase distribution of the generated perfect vortex light and the light field distribution interfered with the Gaussian beam.The fringes of the phase and the interference light intensity reveal the topological charge of the perfect vortex light field.The continuous phase distribution of perfect spiral lens is transformed into the phase distribution with half wave mutation,and the perfect vortex optical field with notch is obtained.The position of half wave mutation determines the position of notch.(3)The equivalent elliptical spiral lens is obtained by replacing the spiral phase plate,spherical lens and diaphragm in the equivalent circular symmetric spiral lens with the elliptical spiral phase plate,lens and diaphragm.When the incident beam is plane wave,the result of formula derivation shows that the outgoing beam is converging,there is Hermitian term in the light field and the phase is spiral distribution,so the light field is elliptical vortex light,MATLAB The simulation results prove this conclusion.The simulation results also show that,when the elliptical aperture is small,the intensity distribution of the light field on the focal plane of the equivalent elliptical spiral lens is elliptical ring;when the elliptical aperture is large,the intensity distribution is light and dark stripes,and the number of dark stripes or light stripes minus one is equal to the topological charge,which is the self-display characteristic of converging elliptical vortex beam.(4)The experimental light path is built to verify the formula derivation of the elliptical spiral lens and the MATLAB simulation results.The experimental and simulation results are very consistent,which proves the correctness of the previous work.